| Date | May 2017 | Marks available | 1 | Reference code | 17M.3.SL.TZ2.1 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Calculate | Question number | 1 | Adapted from | N/A |
Question
A radio wave of wavelength \(\lambda \) is incident on a conductor. The graph shows the variation with wavelength \(\lambda \) of the maximum distance d travelled inside the conductor.
For \(\lambda \) = 5.0 x 105 m, calculate the
The graph shows the variation with wavelength \(\lambda \) of d 2. Error bars are not shown and the line of best-fit has been drawn.
A student states that the equation of the line of best-fit is d 2 = a + b\(\lambda \). When d 2 and \(\lambda \) are expressed in terms of fundamental SI units, the student finds that a = 0.040 x 10–4 and b = 1.8 x 10–11.
Suggest why it is unlikely that the relation between d and \(\lambda \) is linear.
fractional uncertainty in d.
percentage uncertainty in d 2.
State the fundamental SI unit of the constant a and of the constant b.
Determine the distance travelled inside the conductor by very high frequency electromagnetic waves.
Markscheme
it is not possible to draw a straight line through all the error bars
OR
the line of best-fit is curved/not a straight line
Treat as neutral any reference to the origin.
Allow “linear” for “straight line”.
[1 mark]
d = 0.35 ± 0.01 AND Δd = 0.05 ± 0.01 «cm»
«\(\frac{{\Delta d}}{d} = \frac{{0.5}}{{0.35}}\)» = 0.14
OR
\(\frac{1}{7}\) or 14% or 0.1
Allow final answers in the range of 0.11 to 0.18.
Allow [1 max] for 0.03 to 0.04 if \(\lambda \) = 5 × 106 m is used.
[2 marks]
28 to 30%
Allow ECF from (b)(i), but only accept answer as a %
[1 mark]
a: m2
b: m
Allow answers in words
[2 marks]
ALTERNATIVE 1 – if graph on page 4 is used
d 2 = 0.040 x 10–4 «m2»
d = 0.20 x 10–2 «m»
ALTERNATIVE 2 – if graph on page 2 is used
any evidence that d intercept has been determined
d = 0.20 ± 0.05 «cm»
For MP1 accept answers in range of 0.020 to 0.060 «cm2» if they fail to use given value of “a”.
For MP2 accept answers in range 0.14 to 0.25 «cm» .
[2 marks]
